Density self-interaction errors

Perdew, J. P., Ernzerhof, M., 1998, Driving Out the Self-Interaction Error in Electron Density Functioruil Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

Zhang, Y., Yang, W., 1998, A Challenge for Density Functionals Self-Interaction Error Increases for Systems With a Noninteger Number of Electrons , J. Chem. Phys., 109, 2604. 

The simplest way to gain a better appreciation for tlie hole function is to consider the case of a one-electron system. Obviously, the Lh.s. of Eq. (8.6) must be zero in that case. However, just as obviously, the first term on the r.h.s. of Eq. (8.6) is not zero, since p must be greater than or equal to zero throughout space. In die one-electron case, it should be clear that h is simply the negative of the density, but in die many-electron case, the exact form of the hole function can rarely be established. Besides die self-interaction error, hole functions in many-electron systems account for exchange and correlation energy as well. 

With respect to correlation functionals, corrections to the correlation energy density following Eq. (8.29) include B88, P86, and PW91 (which uses a different expression than Eq. (8.27) for the LDA correlation energy density and contains no empirical parameters). Another popular GGA correlation functional, LYP, does not correct the LDA expression but instead computes the correlation energy in toto. It contains four empirical parameters fit to the helium atom. Of all of the correlation functionals discussed, it is the only one tliat provides an exact cancellation of the self-interaction error in one-electron systems. 

The linear photoresponse of metal clusters was successfully calculated for spherical [158-160, 163] as well as for spheroidal clusters [164] within the jellium model [188] using the LDA. The results are improved considerably by the use of self-interaction corrected functionals. In the context of response calculations, self-interaction effects occur at three different levels First of all, the static KS orbitals, which enter the response function, have a self-interaction error if calculated within LDA. This is because the LDA xc potential of finite systems shows an exponential rather than the correct — 1/r behaviour in the asymptotic region. As a consequence, the valence electrons of finite systems are too weakly bound and the effective (ground-state) potential does not support high-lying unoccupied states. Apart from the response function Xs, the xc kernel /xc[ o] no matter which approximation is used for it, also has a self-interaction error. This is because /ic[no] is evaluated at the unperturbed ground-state density no(r), and this density exhibits self-interaction errors if the KS orbitals were calculated in LDA. Finally the ALDA form of /,c itself carries another self-interaction error. 

I. Ciofini, C. Adamo, and H. Chermette (2005) Effect of self-interaction error in the evaluation of the bond length alternation in trans-polyacetylene using density-functional theory. J. Chem. Phys. 123, p. 121102... 

Abstract This chapter discusses descriptions of core-ionized and core-excited states by density functional theory (DFT) and by time-dependent density functional theory (TDDFT). The core orbitals are analyzed by evaluating core-excitation energies computed by DFT and TDDFT their orbital energies are found to contain significantly larger self-interaction errors in comparison with those of valence orbitals. The analysis justifies the inclusion of Hartree-Fock exchange (HFx), capable of reducing self-interactions, and motivates construction of hybrid functional with appropriate HFx portions for core and valence orbitals. The determination of the HFx portions based on a first-principle approach is also explored and numerically assessed. 

The most familiar correction for functionals may be the self-interaction correction, which removes the self-interaction error of exchange functionals. In density functional theory, the self-interaction error indicates Coulomb self-interactions, which should cancel out with the exchange self-interactions but remain due to the use of exchange functionals as a substitute for the Hartree-Fock exchange integral in the exchange part of the Kohn-Sham equation. 

In this correction, assuming homogeneously distributed electrons like those in a uniform electron gas, the self-interaction error is removed by eliminating the Coulomb potential of one electron. Although this potential correction is based on a quite rough assumption, it is used even in chemistry, for example, to derive an exchange-correlation potential from the electron density in the ZMP method (see Sect. 4.5). 

Self-interaction errors are more serious for core orbitals than for valence orbitals. For a-spin self-interacting electrons, which have no electron-electron interaction, the density matrix is represented as... 

There is a general tendency of the DPT methods to overestimate the electton density delocalization. This happens due to self-interaction error [95], The Fe -0 /FeIV=0 competition may also originate from this problem. What is more favorable, charge delocalization over double Fe=0 bond or charge separation. 

Key words Density functional theory - Exchange-correlation functional - Fractional number of electrons -Self interaction error - Derivative discontinuity... 

The earliest example of diabatization by FDE was given in Ref. [48]. This is shown in Fig. 4.1, where the spin densities for a pair of guanines are calculated. KS-DFT of the supersystem carried out with semilocal XC functionals fails in the prediction of the spin density. This is because the self-interaction error makes the spin density spread on both guanines against the prediction given by more accurate theoretical work [35] and experimental studies [99-101]. On the contrary, FDE localizes the charge on a guanine of choice. 

The first of these functionals is the self-interaction corrected LDA (SIC-LDA) [22]. It has been emphasized that the self-interaction error of the LDA and the GGA is a major source of problems. It is thus tempting to try to eliminate this self-interaction in a semi-empirical form. This is the main idea behind the SIC-LDA. The starting point is the spin-density dependent version of the standard LDA, nj,]. In contrast to the exact E c[n, ... 

P. Mori-Sanchez, A. J. Cohen, and W. Yang, /. Ghem. Phys., 125, 201201 1-4 (2006). Many-Electron Self-Interaction Error in Approximate Density Functionals. 

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